One Sunday evening, in the winter of 1981-82, there was a celebration, at the Duke of York's Theatre in London, of the original radio production of Under Milk Wood. Various participants in that famous broadcast, including Richard Burton, the original narrator, were to read the play under the direction of its producer, Reggie Smith. The theatre was packed, with a largely Welsh audience.

Burton seemed to be enjoying himself, but it was not easy to hear him. He was glued to the book, seemingly in private communion with it. After the interval, the reading resumed. It was evident that Burton had liberally refreshed himself. Now he was not just inaudible but incoherent, with a tendency to slump. The reading lurched to its conclusion, after which the cast repaired to the Garrick Club for a celebratory supper. On the appearance of the first course, soup, Burton gracefully slid into the bowl, face first, at which, it is reported, Elizabeth Taylor (who had made a brief and charming unannounced appearance onstage at the beginning of the evening), briskly pulled his head up, wiped him clean and took him back to the Savoy Hotel.

The wonder is that he pulled himself together sufficiently during the two years which remained to him after this incident to act in a number of films, including his last, 1984, shot the year of the title. Except for occasional brief stints on the wagon, these diaries, at least the vastly longer part of them, from 1965 onwards, could well be titled – as Burton himself suggests, only half-humorously – "The Diary of a Dipsomaniac". His consumption is on a heroic scale. In May 1975, for example, there are six consecutive one-word entries: the word is "booze". On the seventh day, the entry reads: "went into clinic late afternoon". It is the familiar alcoholic pattern: the moroseness, the destructiveness, the self-reproach – what he calls "my mad moods".

By the end of the diaries, neither he nor the reader is any nearer to understanding the origins of his addiction. ("I don't know why I drink so much. I'm not unhappy …") On the face of it, he led a blessed life. Born Richard Jenkins in a Welsh mining village, he left it at the age of two after the death of his mother and thus escaped his father's and his grandfather's desperate lives on the coalface, moving to his sister's house in Port Talbot, where he was lovingly raised. At the age of 16, he met his mentor, the English teacher Philip Burton, one of those extraordinary polymaths who choose to lead their lives in obscurity. Their relationship, which gave the boy a superb education, culminated in the 19-year-old Rich becoming Burton's ward, and taking his name.

From then on, against the background of the war and National Service, he moved from one charmed opportunity to another: after a six-month RAF course at Exeter College, Oxford, and demob in 1947, when he was 22, he was signed up as an actor by the greatest producer of his day, Binkie Beaumont. By 1948, he had enjoyed West End and Broadway successes; the following year he made his first film; in 1951, he had his first classical success at Stratford; in 1952 he went to Hollywood, starring opposite Olivia de Havilland; the next year he had two legendary seasons at the Old Vic, which confirmed him as a great classical actor; soon after he was signed by Twentieth Century Fox. In 1957, at the age of 32, and only 10 years after he started acting, he had to become a tax exile because his earnings were so great; he continued to act on stage, creating the part of Arthur in the successful musical Camelot. In 1962, he met Taylor, their relationship ignited, and together they became for many years the epitome of glamour, immeasurably the starriest acting couple of their time.

And all along, we learn from the diaries, Burton was hating every second of it. The acting, that is, not the life. "I like being famous," he cheerfully admits, and he certainly liked being rich (every so often he stops to tot up just how many millions he has), but he detested acting. "I loathe, loathe, loathe acting … hate it, despise it, despise, for Christ's sake, it." Nothing annoyed him more than being asked by a journalist about "his first love, the stage". He berates one of them for not being able to understand "the indignity and the boredom of having to learn the writings of another man", and the situation in which "you are 43 years old, are fairly widely read", and have to "drag yourself off to work day after day with a long lingering regretful look behind you at the book you're interested in".

He sneeringly dismisses the idea of dedication in actors: "Dedication is an invention of envious journalists. It's all right for your Paul Scofield, or Gielgud, or Larry Olivier, or John Neville to 'dedicate' their lives to the theatre, but, poor sods, no other fucker will allow them on the phone." He prides himself on his professionalism, which amounts to his ability to learn lines, to speak them clearly, to speed the process on. But the idea that there might be something more to acting – that acting might be a creative art – is ludicrous to him.

All this is familiar from the writings of Dirk Bogarde, another actor who saw acting as beneath contempt. Like Bogarde, Burton has ambitions to write; unlike Bogarde, all that he wrote was the diary, and then only fitfully. He can write, no question about it, mostly in the allusive style of the insatiable bibliovore, sometimes with the eye of a sharp reporter: there are vivid glimpses of Marshal Tito (whom he played in a film) and of the playful president of Dahomey; there is witty stuff about his fellow-actors: "Rex Harrison wears clothes as only a coat-hanger can. Clothes, no matter how dreadful, drape themselves around him, knowing that they have come home at last." And there is much intimate material, of course, about the woman he sometimes calls "Glorious", sometimes "One-take", now and then "Fatty", once "Slowtake" – Elizabeth Taylor, whom he palpably adores, despite the booze-induced volatility of their relationship. "I was so fed up, I had three glasses of wine and two large brandies in about ½ an hour, ate my pasta, and went to bed. We shouted at each other a bit but nothing serious." They share an attitude, he thinks, to acting, and to life: "Both Eliz and I agreed solemnly that we never want to work again but simply loll our lives away in a sort of eternal Sunday." And then he adds: "Quite right too. We are both bone-lazy."

The reason Burton – unlike Bogarde, with his novels, his autobiographies, his reviews – never fulfils his dreams of writing is that it would involve sustained work. Similarly his vision of teaching at Oxford – teaching medieval poets in English, French, Italian and German, he fantasises – dwindles into a few personal appearances because it requires hard labour, not least having to learn medieval French, Italian and German. He despises all directors – Huston, Losey, Zeffirelli – and knows that he could do it better than they: of Zeffirelli's dazzling The Taming of the Shrew, he vows, while acting in it, that "never again, if I ever have the chance, will I permit anybody to direct something that I know I am better qualified to do." Somehow, he never quite gets round to it, except once, when he co-directs the disastrous Dr Faustus: halfway through filming, he reports: "I am running out of energy and enthusiasm."

And acting is a dreary burden to him for the same reason: he is "simply uninterested in the work". The key to his understanding of acting is in his remark that "my first love … is not the stage, but a book with lovely words in it." And this is in the end why Burton's acting is so disappointing: even when he's trying – especially when he's trying – he's playing neither a character nor an action; he's simply intoning words, narcissistically resonating them through his superb vocal instrument. This is not acting: it is speaking. And this is why Burton found acting so unsatisfying; he was using so little of himself. He is bored by it. The words bore, boring, bored and boredom appear with monotonous regularity throughout the diaries. Maria Callas is a bore. All children, including his own, bore him "after a while". Like a character out of Lermontov or Chekhov, he gazes at the world with ever-dyspeptic eyes.

But why? Whence all this misery? He asks the same of himself. "I am stupendously disappointed in myself. Something went wrong in my head at the wrong time … I am, I think, sublimely selfish." Well, there you have it, although sublime may not be the word that first comes to mind. Meanwhile, whatever the disappointment, there is a great deal of money to made, and to be spent. It is hard not to turn away from the page in disgust as Burton works himself into a competitive frenzy bidding for a diamond that he eventually secures for $1,100,000. He lightly ironises an earlier, less frenzied purchase, crowing over Onassis's paltry expenditure of less than $100,000 on Jackie Kennedy's engagement ring, whereas he, Burton, gave Taylor a £127,000-ring "just because it was a Tuesday".

He is generous to individuals and to institutions, but when he impulsively buys the private jet he's travelling in (an incident quoted on the cover of the book), it simply turns the stomach. The rewards of the world gratify him, though they, too cannot satisfy him. He is quietly pleased with his CBE, knowing that it may lead to a knighthood. "A couple of seasons at the Old Vic and a stint or two at Oxford and I could swing one fairly easily with Labour in power," he muses. But increasingly the booze obliterates both his life and his career. He and Taylor break up, the relationship having turned into something even worse than the one they so vividly depicted in Who's Afraid of Virginia Woolf?

By the end of the diaries, in 1982, he is appearing in Private Lives, with Taylor, long after their second divorce. There is something infinitely sad about the fact that he now finds her, his Cleopatra, with her apparently infinite variety, finally, "boring" too. The diaries were never intended for publication, and it is difficult to imagine why it was thought advisable to present them at this length. Though the book labours under a critical apparatus that might have been thought de trop if the subject had been Wittgenstein, it is not helpful in telling us about, for example, Taylor's father. The notes, pedantic as they are, are also often simply wrong: Wolf Mankowitz spelt his last name with a W, not a V; the "Trumpet Voluntary" is not by Henry Purcell but Jeremiah Clarke. "God save us all and Oscar Wilde," says Burton, and we are solemnly informed that Oscar Wilde was a poet, dramatist and wit (1854-1900), but not the origin of the phrase or what exactly it means. Burton, a keen and highly critical reader, would have had sharp words to say; words were everything to him. He might have made a splendid Graham Greene-ish foreign correspondent, disgusted with the world, risking his life, propping up the bar, filing his copy seconds before the deadline. He was wasted on acting, and acting was wasted on him.

• Simon Callow's Charles Dickens is published by Harper Press.

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